Numerical investigation of plane Couette flow with weak spanwise rotation

Direct numerical simulation of rotating plane Couette flow (RPCF) at Re-w = 1300 and Ro = 0.02 was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid resolution in wall units with x(+) = 8.51, z(+) = 4.26, y(+)|min = 0.0873 and y(+)|(max) = 3.89 is fine enough to simulate the problem at the present parameters. The streamwise length L-x and spanwise length L-z of the computational box have different impacts on the flow statistics, where the statistics were converged if L-x is longer than 8h, while no converged results were obtained for different L-z. More importantly, our results with very long simulation time showed that a state transition would happen if L-x 8h, from a state with four pairs of roll cells to a state with three pairs of roll cells with L-z = 6h. Each state could survive for more than 1500h/U-w, and the flow statistics were different.